We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by diagrammatic Monte Carlo method and the data got through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.
The polaron optical conductivity is derived within the strong-coupling expansion, which is asymptotically exact in the strong-coupling limit. The polaron optical conductivity band is provided by the multiphonon optical transitions. The polaron optical conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate Diagrammatic Quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $α\gtrapprox 9$.
The Momentum Average approximation is used to derive a new kind of non-perturbational analytical expression for the optical conductivity (OC) of a Holstein polaron at zero temperature. This provides insight into the shape of the OC, by linking it to the structure of the polaron's phonon cloud. Our method works in any dimension, properly enforces selection rules, can be systematically improved, and also generalizes to momentum-dependent couplings. Its accuracy is demonstrated by a comparison with the first detailed set of three-dimensional numerical OC results, obtained using the approximation-…
An interacting electron-phonon system is considered within the Extended Holstein model at strong coupling regime and nonadiabatic approximation. It is assumed that screening of an electron-phonon interaction is due to the excess electrons in a lattice. An influence of the screening on the mass and optical conductivity of a lattice polarons is studied. A more general form Yukawa-type electron-phonon interaction potential potential is accepted and corresponding forces are derived in a lattice. It is emphasized that the screening effect is more pronounced at the values of screening radius compara…
Polaron relaxation and hopping conductivity in LaMn$_{1-x}$Fe$_{x}$O$_3$
研究了LaMn $_{1-x}$ Fe $_{x}$ O $_3$（0 $\leq x \leq$ 1.0）样品的直流和交流输运性质以及电模量谱。体直流电阻率示出了与在低温下的可变范围跳跃机制和在高温下的Arrhenius机制一致的温度变化。已经发现，在有限的温度和频率范围内，交流电导率遵循幂律行为，其中安德森局域化在所有组合物的传输机制中起着重要作用。在低温下，所有组合物的大直流电阻率和介电弛豫行为与载流子的极化性质一致。缩放的模量谱表明，电荷传输动力学是独立的温度为一个特定的组合物，但强烈依赖于不同的组合物可能是由于不同的载流子浓度和结构特性。
A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaro…
Recent experimental data on the optical conductivity of niobium doped SrTiO$_{3}$ are interpreted in terms of a gas of large polarons with effective coupling constant $α_{eff}\approx2$. The {theoretical approach takes into account} many-body effects, the electron-phonon interaction with multiple LO-phonon branches, and the degeneracy and the anisotropy of the Ti t$_{2g}$ conduction band. {Based on the Fröhlich interaction, the many-body large-polaron theory} provides an interpretation for the essential characteristics, except -- interestingly -- for the unexpectedly large intensity of a peak a…
Optical conductivity of an interacting polaron gas is calculated within an extended random phase approximation which takes into account mixing of collective excitations of the electron gas with LO phonons. This mixing is important for the optical response of strongly polar crystals where the static dielectric constant is rather high: strontium titanate is the case. The present calculation sheds light on unexplained features of experimentally observed optical conductivity spectra in $n$-doped SrTiO$_{3}$. These features appear to be due to dynamic screening of the electron-electron interaction …
We consider the impact of orbital polarons in doped orbitally ordered systems on optical conductivity using the simplest generic model capturing the directional nature of either $t_{2g}$ (or $e_g$) orbital states in certain transition metal oxides, or $p$ orbital states of cold atoms in optical lattices. The origin of the optical transitions is analyzed in detail and we demonstrate that the optical spectra: (i) are determined by the string picture, i.e., flipped orbitals along the hole hopping path, and (ii) consist of three narrow peaks which stem from distinct excitations. They occur within …
The optical properties of magnetite at room temperature were studied by infrared reflectivity measurements as a function of pressure up to 8 GPa. The optical conductivity spectrum consists of a Drude term, two sharp phonon modes, a far-infrared band at around 600 cm$^{-1}$, and a pronounced mid-infrared absorption band. With increasing pressure both absorption bands shift to lower frequencies and the phonon modes harden in a linear fashion. Based on the shape of the MIR band, the temperature dependence of the dc transport data, and the occurrence of the far-infrared band in the optical conduct…
Reflectivity as a function of temperature for the La$_{0.67}$Ca$_{0.33}$MnO$_{3}$ (LCMO) film has been measured across the metal-insulator phase transition. The optical properties and their temperature dependence were determined in the infrared and visible range by fits to a Drude-Lorentz model, using exact formula for the thin film optics and the measured properties of the substrate. The phonon modes were identified and verified with lattice dynamical calculations for the ideal and distorted perovskite structure of the material. The optical conductivity shows agreement with the double exchang…
The optical properties of a V4O7 single crystal have been investigated from the high temperature metallic phase down to the low temperature antiferromagnetic insulating one. The temperature dependent behavior of the optical conductivity across the metal-insulator transition (MIT) can be explained in a polaronic scenario. Charge carriers form strongly localized polarons in the insulating phase as suggested by a far-infrared charge gap abruptly opening at T_MIT = 237 K. In the metallic phase instead the presence of a Drude term is indicative of fairly delocalized charges with a moderately renorm…
We describe the formation and properties of Holstein polarons in the entire parameter regime. Our presentation focuses on the polaron mass and radius, which we obtain with an improved numerical technique. It is based on the combination of variational exact diagonalization with an improved construction of phonon states, providing results even for the strong coupling adiabatic regime. In particular we can describe the formation of large and heavy adiabatic polarons. A comparison of the polaron mass for the one and three dimensional situation explains how the different properties in the static os…
Temperature-dependent angle-resolved photoemission spectroscopy (ARPES) was carried out on single-crystalline EuB6 samples. By measuring ARPES spectra in an extended Brillouin zone, a B 2p hole pocket centered at the X point is clearly observed, thus proving the semimetallic nature of EuB6. Below the Curie temperature TC, ARPES spectra show two B 2p bands of which separation is due to an exchange interaction between local Eu 4f and itinerant B 2p electrons. The exchange splitting becomes smaller as the temperature increases and disappears well above TC. Additionally, a diffuse structure near t…
YTiO3, as a prototypical Mott insulator, has been the subject of numerous experimental investigations of its electronic structure. The onset of absorption in optical conductivity measurements has generally been interpreted to be due to interband transitions at the fundamental gap. Here we re-examine the electronic structure of YTiO3 using density functional theory with either a Hubbard correction (DFT+U) or a hybrid functional. Interband transitions turn out to be much higher in energy than the observed onset of optical absorption. However, in case of $p$-type doping, holes tend to become self…
Electric conductivity and structural details of the hole-doped polaron conductor La0.9Sr0.1FeO3 (LSF10) are reported. The conductivity of a single crystal shows an exponential increase with temperature with a maxi-mum of 100 S/cm at 700 K and with activation energy of about 375 meV, and a decrease for higher temperatures that follows a power law. The exponential increase of the electric conductivity for 300 K {\leg} T {\leg} 700 is accompanied by a shift of spectral weight in the photoemission valence band towards the Fermi level, indicative of a strong electron-phonon interaction. The subsequ…
We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength $λ$, in all models where this coupling depends only on phonon momentum $q$. In the SSH model the coupling also depends on the electron momentum $k$; we find it has a sharp transition, at a critical coupling strength $λ_c$, between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at…
Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
We investigate the effect of local electron-phonon coupling on nonlinear optical conductivity in an interacting ferroelectric system. Using real-time simulations, we show an enhancement in nonlinear conductivity under linearly-polarized light due to generation of the phonon-assisted ballistic-current in addition to the injection-current generated by electron-hole pairs. The optically excited phonon modes generate an asymmetric carrier distribution that causes a strong directional ballistic-current. The ballistic-current enhances the photocurrent several times at above band-gap excitation frequ…
We present exact diagonalization and momentum average approximation (MA) results for the single polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=π$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-b…
We investigate the electronic properties and electron correlations in a three-dimensional (3D) polaron system with tunable dispersion parameter in Fermi-liquid picture. The polaronic coupling is considered as a weakly attractive bare coupling. Both the single and many-polaron, zero and finite-temperature cases are considered in this paper. The physical quantities, including the self-energy, spectral function, optical conductivity (both the planar and 3D one), free energy, and momentum distribution function, are studied and are been verified exhibit Fermi-liquid features. Both the analytic deri…
The three band p-d model of strongly correlated electrons interacting with optical phonon via diagonal and off-diagonal electron-phonon interaction is considered within cluster perturbation theory. At first step the exact diagonalization of the Hamiltonian of CuO4 cluster results in the construction of local polaronic eigenstates |p> with hole numbers nh=0,1,2 per unit cell. The inter cluster hoppings and interactions are exactly written in terms of Hubbard operators X(pq)= |p><q| determined within the multielectron polaronic eigenstates |p>. The Fermi type single electron quasiparticle disper…
Electron-phonon coupling, diagonal in a real space formulation, leads to polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if non-diagonal pairing is involved into consideration. The study of polaron transformations and related properties of matter is of particular interest for realistic models, since competition between diagonal and non-diagonal electron-phonon contributions in the presence of other strong interactions can result in unconventional behavior of the system. Here we consider the multiband pd-model of cup…
In this work, we explore the polaron and molecule physics by utilizing a unified variational ansatz with up to two particle-hole(p-h) excitations(V-2ph). We confirm the existence of a first-order transition in 3D and 2D Fermi polarons, and show that the nature of such transition lies in an energy competition between systems with different momenta ${\mathbf Q}=0$ and $|{\mathbf Q}|=k_F$, here ${\mathbf Q}$ is defined as the momentum of Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum $k_F$). The literally proposed molecule ansatz is identified as an a…
We present the first approximation free diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground state properties, spectral function, and optical conductivity. The unique feature of such polaron is the interplay between long- and short wavelength acoustic vibrations creating a composite phonon cloud and leading to persistent self-trapping due to the existence …
LaFe3/4Ni1/4O3 was subjected to oxygen near edge x-ray absorption fine structure (NEXAFS) spectroscopy for 300 K < T < 773 K. The spectra show in the pre-edge a small hole doped peak originating from Ni substitution. The relative spectral weight of this transition to the weight of the hybridized O(2p) - Fe(3d) transitions scales with T and has a maximum at around 600 K. The characteristic energies of the thermal activated spectral intensity and conductivity suggest that the concentration of charge transferred electrons from O(2p) to Ni(3d) increases and that the pre-edges account in part for t…
Keeping the full quantum nature of the problem we compute the relaxation time of the Holstein polaron after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse the polaron's kinetic energy increases and subsequently exhibits relaxation type decrease with simultaneous emission of phonons. In the weak coupling regime partial tunneling of the electron from the polaron self-potential is observed. The inverse relaxation time is for small values of electron-phonon coupling $λ$ linear with $λ$, while it deviates downwards from the linear regime at $λ\gtrsim 0.1/…
Motivated by the problem of polaron effect due to phonon-modulated hopping, we formulate a generic Monte Carlo technique for solving it in the coordinate representation for both the particle and atomic displacements. The method applies to a broad class of models; the only condition is that the hopping amplitude be sign-positive. A dramatic simplification of the scheme, with the corresponding efficiency gain, takes place in models with dispersionless phonons. Our study sheds important light on the nature and universality of the most striking qualitative and quantitative effects demonstrated by …
We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the…
We theoretically study magnon-phonon hybrid excitations in a square lattice ferromagnet subjected to a magnetic field by varying the field direction. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are investigated by considering all three phonon modes: vertical phonon, transverse phonon, and longitudinal phonon. We show that the topological proprieties of three hybridizations are different in terms of the Berry curvature and the Chern numbers. We also find that the topological properties of the bands can be controlled by changing the direction of the magnetic f…
We theoretically investigate magnon-phonon hybrid excitations in two-dimensional ferromagnets. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are analytically shown to be topologically nontrivial, possessing finite Chern numbers. We also show that the Chern numbers of magnon-polaron bands and the number of band-crossing lines can be manipulated by an external magnetic field. For experiments, we propose to use the thermal Hall conductivity as a probe of the finite Berry curvatures of magnon-polarons. Our results show that a simple ferromagnet on a square lattice…
